In my board I have used a 22uF/35V tantalum capacitor (125E ESR). It is across the filtered output of bridge wave rectifier. So it is rippled DC. The peak voltage across it is 25V under worst condition.

When I turned on the power supply, the capacitor got burnt immidiately (shorted). Now I am analysing what went wrong? I have checked, max volateg across it, temperature etc. I am told to check the ripple voltage to ripple current. How to measure it with CRO?

Adding to Beenthere's suggestion, you will find that while most aluminum electrolytic capacitors have their - side marked, tantalum capacitors have their + side marked. This can easily lead to confusion (and loud BANGs) if you're simply looking for a mark.

It is best to check the manufacturer's datasheet to verify what their particular marks mean.

(1) For general applications, apply 70% or less of the rated voltage to the capacitor.
(2) When the capacitor is used in a power line or a low-impedance circuit, keep the applied voltage within 30% (50% max.) of the rated voltage to avoid the adverse influence of inrush current.

We will keep the 50% derating factors as a recommended practice for
the MnO2 cathode system tantalums; but for the polymer-based cathode systems
of the T520 and T530 series of the KO-CAP tantalum capacitors, we will
recommend a 20% derating factor. This will allow the capacitors to be used at 80% of the rated volt age.

In my board I have used a 22uF/35V tantalum capacitor (125E ESR). It is across the filtered output of bridge wave rectifier. So it is rippled DC. The peak voltage across it is 25V under worst condition.

When I turned on the power supply, the capacitor got burnt immidiately (shorted). Now I am analysing what went wrong? I have checked, max volateg across it, temperature etc. I am told to check the ripple voltage to ripple current. How to measure it with CRO?

Thanks in advance.

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Is this tantalum capacitor being used to pre-filter the voltage at the input to a switching mode power supply?

Firstly, I will qualify my remarks by saying I don't like dipped tantalum caps at all and won't use them at all if I can help it. The tantalums I have experience with are hermetically sealed (wet) types and I haven't used the polymer types yet.

Tantalum capacitors (wet) are characterised by extremely low ESR, high temperature operation (>125C), with long and reliable life (are used in medical and space apps). I do use them in DC filtering, but only with certain provisos;

They don't like high ripple or where the likelihood of high surge currents are present and I never use them on their own as a filter directly after an ac rectifier arrangement. I use them only on a regulated DC supply as an adjunct to a good quality aluminium electrolytic bulk storage capacitor and I haven't ever had one fail in this application mode.

This Kemet paper gives some pertinent information as to the failure of tantalum caps in power on surge situations and the use of Surge Step Stress Testing.
http://www.kemet.com/kemet/web/homepage/kfbk3.nsf/vaFeedbackFAQ/B015828EE4AFF1808525722500694AD4/$file/2001%20CARTS%20SSST.pdf